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Closed and open pipes of the same length give beats in their first overtone; the lengths are changed; find the new number of beats

The same question, asked 2 times: 20 Apr 2025 S2*, 26 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    20 Apr 2025 S2

    13
    The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce 3 beats. The length of open pipe is made (13)rd \left( \frac{1}{3} \right)^{\text{rd~}} and that of closed pipe is made 3 times the original, the number of beats produced will be (Neglect end correction)

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  2. Question 2

    26 Apr 2025 S2

    45
    The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, they produce four beats. The length of open pipe is made half and that of the closed pipe is made two times the original. Now the number of beats produced if the two pipes are vibrating in their fundamental modes simultaneously is

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